Question

se considera nnr a =26²⁰¹⁶+2×26²⁰¹⁷+26²⁰¹⁸ a)Aratati ca nr a este patrat perfect si cub perfect
b)Demonstrații ca nr b= a:(81×32⁴⁰²×169¹⁰⁰⁴)este nr natural
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Answer 1

Explicație pas cu pas:

a=26^2016+2×26^1×26^2016+26^2×26^2016=(1+2×26+26^2)×2^2016=(1+26)^2 × [26^1008]^2 = [27×26^1 008]^2

deci a este patrat perfect

a=[3^3×26^(3×336)]^2 =[3^2 ×26^(2×336)]^3

deci a este si cub perfect

a=3^6×(2×13)^2×3×336=3^2×3^4×2^2016×(13^2)^1008=3^2×81×2^2016×169^1008

32^402=(2^5)^402=2^2010

b=a:[81×2^2010×169^1004]=3^2×2^6×169^4

care evident este natural